Adaptive control convergence has been proved for long time by using slow switching schemes through separating the two successive switching events by a positive time interval (e.g., dwell-time, average dwell-time, hysteresis switching technique). This thesis addresses the inherent limitations of some logic-based switching among infinite (i.e. continuum) set of candidate controllers. In this thesis, we examine adaptive control convergence in the context of well-known hysteresis switching algorithm by relaxing the usual requirement that the hysteresis constant is strictly positive. Relaxing this constraint allows the adaptive controller to converge to a unique optimum in the case of an infinite (continuum) candidate controller set, provided that at least one controller in the controller set has the ability to satisfy adaptive control performance.
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